Over the past few months there have been quite a few departures at my place of work. It's a combination of things. Some people have been terminated, some people have left for other jobs (or no job), some people were laid-off when the company was acquired. I've received a lot of feedback about announcing these departures and it's a complicated subject.
The different types of departures ask for different treatments. In addition, I often ask people who are leaving (at least under good circumstances) what they would like to do. The treatment of the departure is many times at their choice.
The usual feedback is that people "disappear." That is to say that we don't announce the departure of the reason. Let's look at the various case:
1. People Are Terminated for Performance or Behavior
If it were all up to me, after someone is terminated I would send a note to the affected organization (e.g. team/department) letting people know that an employee is no longer with the company. I wouldn't say that the person was terminated, but it might be clear by lack of other information (see more info, below). This trouble with this approach is you always miss someone who is affected (unless you are very small as an entire company and let everyone know).
2. People Leave Voluntarily
In this case, I usually get a couple of weeks of notice. I ask people to let anyone they want to know directly know within a day, so that they can deliver personal news, followed by my need to announce to the affected team and get people moving on knowledge sharing and transfering tasks. Then I ask the person if they'd like me to host a lunch or happy hour to celebrate the next step in their career. Some say yes, some say no. I always leave it to that person.
I don't encourage the "bye everyone" email and it often gets a bit to clever for my taste, but I do send a final note a few days before departure (or day of) to make sure everyone knows the person is leaving that may be affected and give a last chance to have a conversation about work.
3. People Are Laid-Off
In my experience, in this case the timing is very short and you cannot possibly give notice to many (if any people). Again, if it were all up to me, I would sent a combined note about people who are no longer with the company and who their assigned back-ups are.
Fundamentally, there is no easy way to announce someone leaving and there are no correct answers. Balancing the needs of the person leaving and of those staying is difficult. People need to respect each other's privacy without viewing a lack of total transparency as a conspiracy or sign of anything more than mutual respect for privacy.